Spectral collocation methods for nonlinear coupled time fractional Nernst–Planck equations in two dimensions and its convergence analysis

In this paper, a nonlinear coupled time fractional Nernst–Planck equation in two dimensions space is considered. Using properties of the Caputo fractional derivative and Riemann–Liouville fractional integral, the time fractional Nernst–Planck problem is transformed into a Volterra integral model with singular kernel equivalently. We propose a novelty spectral collocation method in time and space with a spectral expansion of Jacobi interpolation polynomial to discretize the model. We also derive the optimal rate of convergence of this method. Numerical results are presented to verify efficiency of collocation methods and spectral accuracy theory.